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Some people have nightmares that they've missed work or shown up late for an exam. But something else may be keeping the co-founder of  Apollo Global Management up at night.

Sitting on the stage at the Bloomberg Invest Conference on Tuesday, The Carlyle Group's co-founder and co-executive chairman David Rubenstein asked Apollo's Leon Black if he had any regrets about taking the firm public.

"Regrets? Absolutely," Black replied.

"The public market doesn't understand creatures like us very well."

He described consulting a dozen investors he respected when deciding whether to go public, including Michael Milken, Carl Icahn, Marty Lipton and Lloyd Blankfein. The consensus among the group was split: Half said it would be a good idea, as it would let the firm monetize its equity, grow globally and add compensation incentives for employees. The other half said that the regulatory scrutiny it would bring wouldn't be worth it.

In the end, Black said that he based his final decision on wanting to grow Apollo out of its domestic scope in the US—something that wouldn't be possible without public investment.

But that decision has seemingly come to haunt him. Shares of Apollo, as well as the other big public PE firms such as  KKR, Blackstone, and Carlyle, have underperformed significantly relative to the S&P and other public indices. Since going public in March 2011, Apollo's stock, for example, has only risen about 69%, compared with 255% for the S&P 500 index, according to FactSet data cited by MarketWatch.

If you ask Black, the market is wrong.

"I think we trade at half where we should be," Black said. "It's not just true of us; it's true of Blackstone and others."

However, change could be on the horizon. One potential reason given for the relatively poor performance of private equity on the public markets is the firms' structure as partnerships rather than C-Corporations. PE firms have long complained that their shares are perpetually undervalued, citing the lack of access to public indices and mutual funds, as well as the complex financials and forms.

But now that the corporate tax rate has fallen from 35% to 21%, it makes more sense to shift. In May, Apollo became the latest big firm to announce its change to a C-Corp structure, following just a few weeks behind Blackstone's announcement. Besides making it easier for the everyday investor to buy shares, it also allows the firm's shares to be included in index funds, opening them up to a massive amount of money being invested passively by investors through institutions or retirement funds.

It remains to be seen how the change will affect the performance of the firm's shares, but early indications are promising. According to a recent PitchBook analyst note, firms that switched to C-Corp status in 2018, such as KKR, have outperformed the share prices of those that haven't by 30%—numbers that are likely music to Black's ears.

The headline of this post has been changed to note that Black said he has some regrets about taking the firm public.

Featured image via JONGHO SHIN/iStock/Getty Images Plus